Some Properties of Density Functions on Maxima of Solutions to One-Dimensional Stochastic Differential Equations

研究成果: Article査読

抄録

This article proves some properties of the probability density function concerning maxima of a solution to one-dimensional stochastic differential equations. We first obtain lower and upper bounds on the density function of the discrete time maximum of the solution. We then prove that the density function of the discrete time maximum converges to that of the continuous time maximum of the solution. Finally, we prove the positivity of the density function of the continuous time maximum and a relationship between the density functions of the continuous time maximum and the solution itself.

本文言語English
ページ(範囲)1746-1779
ページ数34
ジャーナルJournal of Theoretical Probability
32
4
DOI
出版ステータスPublished - 2019 12 1

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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